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Primes p such that p^2 = 6*q + 7, where q is prime.
2

%I #10 Aug 02 2024 02:58:34

%S 5,7,11,17,19,29,37,43,47,53,61,71,73,79,89,97,101,107,109,127,173,

%T 191,199,223,241,251,263,271,281,317,367,389,397,433,439,443,449,457,

%U 461,479,523,541,569,577,587,613,631,647,659,677,683,691,701,739,757

%N Primes p such that p^2 = 6*q + 7, where q is prime.

%H Amiram Eldar, <a href="/A110587/b110587.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = sqrt(A110586(n)). - _Amiram Eldar_, Aug 02 2024

%e a(4) = 17 since 17^2 = 289 = 6*47 + 7.

%p ispower := proc(n,b) andmap(proc(w) evalb(w[2] mod b = 0) end, ifactors(n)[2]) end: a:=6: SQP||a:=[]: for z from 1 to 1 do for n from 1 to 1000 do p:=ithprime(n); m:=a*p+a+1; if ispower(m,2) and isprime(sqrt(m)) then SQPW||a:=[op(SQP||a),sqrt(m)] fi od; od; SQP||a;

%t Select[Prime[Range[135]], PrimeQ[(#^2-7)/6] &] (* _Amiram Eldar_, Aug 02 2024 *)

%o (PARI) is(p) = isprime(p) && !((p^2-7) % 6) && isprime((p^2-7)/6); \\ _Amiram Eldar_, Aug 02 2024

%Y Cf. A110014, A110015, A110016, A110586.

%K nonn,easy

%O 1,1

%A _Walter Kehowski_, Sep 13 2005